Exercise 49 Page 204

To evaluate the determinant of a 3* 3 matrix, we use the diagonal rule.

1. Rewrite the first two columns to the right of the determinant.
2. Draw diagonals, beginning with the upper-left number. Multiply the numbers in each diagonal.
3. Repeat the second step, this time beginning with the upper-right number.
4. Find the sum of the products of the numbers in each set of diagonals, and subtract the second sum from the first.

Let's do it!

Step 1

We will write the given determinant and copy the first two columns on the right-hand side.

Step 2

Now, we will draw diagonals beginning with the upper-left number.

Let's multiply the numbers in each diagonal. 8*5* 9 &= 360 6* 1 *( -3) &= -18 -1*( -4)*(-2) &= -8

Step 3

We will repeat the previous step, but draw diagonals beginning with the upper-right number.

As we did before, let's multiply the numbers in each diagonal. -3*5*(-1) &= 15 -2* 1 * 8 &= -16 9*( -4)* 6 &= -216

Step 4

Finally, we will find the sum of the products in each set of diagonals. Then we will subtract the second sum from the first sum.